Conceptual knowledge maps for mathematics

About working and studying, the main topic of this blog: well, it is no longer an option. It is mandatory, society needs people who are committed to their jobs and invest in their lifetime education. Everything changes at an ever faster pace and it is thus our responsibility to stay of value in all of our dynamics.  It is an issue we must align regularly.

Studying in a particular field will gradually align your life to your new interests. For example, I have recently, more or less -landed- in a job where some of my colleagues are mathematicians. In fact, a lot of the work I do involves mathematics. More about that in posts to come.

Everything changes. So do study skills. And a vast amount of tools for computer aided learning is now available. From MIT lectures via YouTube to software for flash cards to sophisticated knowledge databases for personal use. I would like to mention two items I have found recently.

InfoRapid Knowledge Builder is a graphical tool to document conceptual knowledge maps, free for personal use at http://www.buildyourmap.com/. ( Before this I used Mindjet and TheBrain. ) I am working on a map with topics in Analytical Number Theory.

Another item I found is a book. It is called On Course, Strategies for success in College and Life. ( And if you work and study read the title as Strategies for successful combining work and study.) The book is packed with information. It is not a book you should read once but it is a companion you can use, consult, for years. I have the Study Skills Plus edition.

Fixing mathematics education

Conrad Wolfram spoke about math education at the 2010 Wolfram Technology Conference:

Now, a new initiative has been recently announced at computerbasedmath.org to build a completely new math curriculum with computer-based computation at its heart.

Also see Conrad's Wolfram blog here where he announces that Estonia will be the first country that will completely rewrite their mathematics school curriculum.

One day left...

to vote for the most important British innovation of the 20th Century. Alan Turing's Turing Machine is currently on 2nd place with 13% of the votes.

Vote here.

Filling a bottle...

A professor stood before his philosophy class and had some items in front of him. When the class began, he wordlessly picked up a very large and empty mayonnaise jar and proceeded to fill it with golf balls. He then asked the students if the jar was full. They agreed that it was. The professor then picked up a box of pebbles and poured them into the jar. He shook the jar lightly. The pebbles roll ed into the open areas between the golf balls. He then asked the students again if the jar was full. They agreed it was. The professor next picked up a box of sand and poured it into the jar. Of course, the sand filled up everything else. He asked once more if the jar was full.. The students responded with a unanimous ‘yes.’ The professor then produced two Beers from under the table and poured the entire contents into the jar effectively filling the empty space between the sand.The students laughed.. ‘Now,’ said the professor as the laughter subsided, ‘I want you to recognize that this jar represents your life. The golf balls are the important things—-your family, your children, your health, your friends and your favorite passions—-and if everything else was lost and only they remained, your life would still be full. The pebbles are the other things that matter like your job, your house and your car.. The sand is everything else—-the small stuff. ‘If you put the sand into the jar first,’ he continued, ‘there is no room for the pebbles or the golf balls. The same goes for life. If you spend all your time and energy on the small stuff you will never have room for the things that are important to you. Pay attention to the things that are critical to your happiness. Spend time with your children. Spend time with your parents. Visit with grandparents. Take your spouse out to dinner. Play another 18. There will always be time to clean the house and mow the lawn. Take care of the golf balls first—-the things that really matter. Set your priorities. The rest is just sand. One of the students raised her hand and inquired what the Beer represented. The professor smiled and said, ‘I’m glad you asked.’ The Beer just shows you that no matter how full your life may seem, there’s always room for a couple of Beers with a friend. ( Anonymous )

Happy New Year

Thank you for following The Mathematics Blog in 2012. 

December 25th - Sir Isaac Newton ( Day )

Sir Isaac newton (1642-1727), mathematician and physicist and  the 25th of December is Newton's birthday.

Maybe, some day in the future, when all religion is forgotten ( or banned ) it turns out that we kept the good things, like Holidays and presents. In that future the people may very well celebrate Newton Day on December 25th.

Ironically Newton was deeply devoted to religion all his life.

Computers are simple

Computers are simple. They must be. Consider how fast the industry developed and the only conclusion you can draw is that it must be simple. Once you understand how easy it is to implement the basic operations add, move, compare and jump to a machine, and that you can build -any- program from these operations you'll know. Alan Turing started it all.

The smartphones of today are so much more powerful than the mainframes banks had in the sixties and seventies in terms of computing power. Over a billion people on Planet Earth live with a computer. These computers connect us with other people and are turning into our best friends. And that is something what was beyond what Alan Turing foresaw about computers.

Computer Science and Mathematics students need a deep understanding of the Turing Machine. OU M381 did not teach the Turing Machine but a slightly simpler model because the Turing Machine was considered too complex. Not anymore with today's simulators if you ask me.

Turing Machine simulator

Martin Gardner

Every mathematician knows Martin Gardner. In his days Martin Gardner made mathematics cool. Many great names in mathematics honored him in one way or the other. Gardner wrote about mathematics in a way that appealed to a wide audience. He wrote a column about mathematics in the Scientific American and published more than 100 books.

Meet Martin Gardner in The Nature of Things. ( Vumeo 45min ).

Marty Leeds about PI

Marty Leeds ( http://www.martyleeds33.com/ ) is mathematics fanatic, one of his interests is the number PI. He wrote the books ‘Pi – The Great Work’ en ‘Pi & The English Alphabet’. I called him a math fanatic and not a mathematician because his interest in PI isn't particularly Number Theoretic...

Anyway, he was interviewed by Pateo Radio yesterday ( November, 5 2012 ) http://www.argusoog.org/pateo-radio-05-november-2012/. In case you are interested in PI from a different angle. Enjoy.

Learning by doing.

I hated school, it felt like prison. I never learned a thing in class. I passed the exams thanks to self-study mostly. What is the point in repeating what is in the textbooks? Students can read, can't they? Teachers can and should do better. To my surprise I read this article about a ' revolution ' in mathematics teaching. A revolution?!

Revolution in mathematics teaching

Chris Finlay's Blog

Chris Finlay has more degrees than blogs but here is his blog: http://chrisfmathsphysicsmusic.blogspot.com/

P.S.
I owe Chris a Thank You. He knows why.

A beautiful ( Norwegian ) theorem

#mathematics# #norway#

Theorem:

Every abelian group is the direct product of its Sylow subgroups.

Perhaps it is not the theorem in itself I like so much but what this theorem illustrates about the nature of mathematics. Most laymen think of mathematics as the scribbles of physicists they see in science documentaries, i.e. partial differential equations, stuff they call 'formulas'. So in that sense the theorem above may not even be recognized as mathematics, let alone beautiful mathematics.

Mathematics starts with a very precise, razor blade sharp, use of the tool that differentiates us humans from the rest of nature: language. Einstein once said “If you can't explain it to a six year old, you don't understand it yourself.” (*). He must have meant the "root of your knowledge tree", I suppose. Because the beauty of the theorem lies in what it represents: a large graph of concepts with - ( abelian ) group, direct product and ( Sylow ) subgroup - in the center. To anyone 'owning' these concepts the particular relation between an abelian group and its Sylow subgroups can be described in one sentence with no room whatsoever for misinterpretation. The construction of all that knowledge is the collective work of thousands and thousands of mathematicians before us.

P.S.
(*) The simplest way to explain a group is ( as far as I know ) "A collection of movements with no visible effects ( = symmetries )".

Sylow

Both Abel and Sylow were Norwegians. So was Lie, another giant, a special branch in group theory is named after him: Lie Group Theory. It is amazing that a small country like Norway ( measured in population ) can have such an impact.